Large deviations and transition between equilibria for stochastic Landau-Lifshitz equation

Beniamin Goldys, Zdzisław Brzeźniak and Terence Jegaraj

Abstract

We study a stochastic Landau-Lifshitz equation on a bounded interval and with finite dimensional noise; this could be a simple model of magnetisation in a needle-shaped domain in magnetic media. We obtain a large deviation principle for small noise asymptotic of solutions using the weak convergence method. We then apply this large deviation principle to show that small noise in the field can cause magnetisation reversal and also to show the importance of the shape anisotropy parameter for reducing the disturbance of the magnetisation caused by small noise in the field.

Keywords: stochastic Landau-Lifschitz equation, strong solutions, maximal regularity, large deviations, Freidlin-Ventzell estimates.

AMS Subject Classification: Primary 35K59; secondary 35R60, 60H15, 82D40.